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Evgen [1.6K]
3 years ago
9

Find all the points on the curve y = 4x^4 − 8x^2 + 16x + 7 such that the tangent line to the curve is parallel to the line 16x −

y + 5 = 0.
Mathematics
1 answer:
IrinaVladis [17]3 years ago
4 0
Hello : 
the tangent has same slope of the line 16x -y +5 = 0  because parallel.
y = 16x + 5 
the slope is : 16
but : f'(x) = 16
f'(x) = 16x^3 - 16x +16
solve : 16x^3 - 16x +16 = 16
x^3 - x +1 =1
x^3 - x = 0
x(x² - 1 ) =0
x(x -1 )(x +1) =0
x=0 or x-1 =0 or x +1= 0
x=0 or x = 1 or x = -1
if : x = 0 : y = 4(0)^4 -8(0)^2+16(0) +7 =7
if : x =1 : y = 4(1)^4 -8(1)^2+16(1) +7 = 19
if : x = -1 : y = 4(-1)^4 -8(-1)^2+16(-1) +7 = -13
<span>the points : A(0,7)  , B(1 , 19) , c ( -1 , -13)</span>

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Drag each tile to the correct box. Each tile shows an investor's tax bracket along with the tax-free yield of a bond the investo
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The tax bracket and tax-free yield will be (18%, 3%) < (32%, 3%) < (32% , 4%) < (22% , 5%) < (24% , 6%) .

<h3>Taxable equivalent yield based problem:</h3>

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= Tax-free yield / (100 - Tax bracket)

Taxable equivalent yield =  3 / (100 - 18) = 0.03659

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Taxable equivalent yield = 4 / (100 - 32) = 0.05882

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5 0
2 years ago
Bill's Bargains sells 16 ounces of Circle O's cereal for $3.36. Debbie's Deals sells 40 ounces of Circle O's cereal for $7.60. W
astraxan [27]

Answer:

Debbie's Deals has the better deal with a price of $0.19 per ounce compared to Bill's Bargains at $0.21 per ounce.

Step-by-step explanation:

Divide $3.36 by 16 = $0.21

Divide $7.60 by 40 = $0.19

Debbie's Deals sells the Circle O's cereal for a cheaper per ounce price thus it's the better price and the better deal.

Good luck!

7 0
3 years ago
Batman took a bicycle trip. In all, he traveled 6 hours at a rate of 28 mph. What was his total distance ?
Mice21 [21]
Distance=speed x time
so it would be 28 x 6=168
7 0
3 years ago
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Find the sum or difference (5b-9)-3(8-2b)
True [87]
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3 years ago
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Plz solve the 7th question immediately ....Help me......
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Answer:

The value of x is 8cm. The length of 3 sides are 8cm, 15cm and 17cm.

Step-by-step explanation:

Using Pythagoras' Theorem, a²+b² = c² :

Let a be x cm,

Let b be x+7 cm,

Let c be 2x+1 cm

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Then, move all the variables to one side and solve it to find the value of x :

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= 17 cm

3 0
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